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A theorem you have surely never heard of

Given a regular 11-gon. Consider the diagonals shown above. They are concurrent, that is, they meet at the same point... or not?
Well, they actually don't. So you surely haven't heard of this theorem, because this is a false statement. But, if you were about to prove that these diagonals are not concurrent, how would you do that? Zooming into the figure may be one method... but is it accurate? Do you trust GeoGebra's numerical background and computational correctness? And in general, how deep zoom may be required? Another possibility is to construct this figure with GeoGebra and use the ProveDetails command to learn the truth.